Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram is based on an illustration from Samuel Cunn’s Euclid’s Elements of Geometry (London 1759, Spherical Trigonometry). It illustrates Propositions 25, 26, 27, 28, 29, and 30 on Spherical Trigonometry. Cunn describes Proposition 25 as ‘In a spherical triangle A B C, right-angled at A, as the cosine of the angle B, at the base B A, is to the sine of the vertical angle A C B, so is the cosine of the perpendicular, to the radius’;1 Proposition 26 as ‘The cosine of the base : cosine of the hypothenuse : R :: cosine of the perpendicular’;2 Proposition 27 as ‘S, of the base : R :: T, of the perpendicular : T, of the angle at the base’; Proposition 28 as ‘cosine of the vertical angle : R : : T, of the perpendicular : T, of the hypothenus’;3 Proposition 29 as ‘S, of the hypothenus : R :: S, of the perpendicular : S, of the angle at the base’;4 and Proposition 30 as ‘R : cosine of the hypothenus : : T, of the vertical angle : cot. of the angle at the base’.5 There are sketches of the diagram in Turner’s lecture notes.6
Blank, save for an inscription by an unknown hand in pencil ‘23’ bottom left.
Supported by The Samuel H. Kress Foundation